相关论文: Toric Fano varieties associated to building sets

This article gives an overview of toric Fano and toric weak Fano varieties associated to graphs and building sets. We also study some properties of such toric Fano varieties and discuss related topics.

We give a necessary and sufficient condition for the nonsingular projective toric variety associated to a finite simple graph to be Fano or weak Fano in terms of the graph.

We give a necessary and sufficient condition for the nonsingular projective toric variety associated to a building set to be weak Fano in terms of the building set.

We give a necessary and sufficient condition for the nonsingular projective toric variety associated to the graph cubeahedron of a finite simple graph to be Fano or weak Fano in terms of the graph.

We give a structure theorem for n-dimensional smooth toric Fano varieties whose associated polytope has "many" pairs of centrally symmetric vertices.

In this paper, we consider terminal reflexive polytopes arising from finite directed graphs and study the problem of deciding which directed graphs yield smooth Fano polytopes. We show that any centrally symmetric or pseudo-symmetric smooth…

We investigate Gorenstein toric Fano varieties by combinatorial methods using the notion of a reflexive polytope which appeared in connection to mirror symmetry. The paper contains generalisations of tools and previously known results for…

In this paper, we obtain a complete classification of smooth toric Fano varieties equipped with extremal contractions which contract divisors to curves for any dimension. As an application, we obtain a complete classification of smooth…

A directed edge polytope $\mathcal{A}_G$ is a lattice polytope arising from root system $A_n$ and a finite directed graph $G$. If every directed edge of $G$ belongs to a directed cycle in $G$, then $\mathcal{A}_G$ is terminal and reflexive,…

We exhibit full exceptional collections of vector bundles on any smooth, Fano arithmetic toric variety whose split fan is centrally symmetric.

We obtain 866 isomorphism classes of five-dimensional nonsingular toric Fano varieties using a computer program and the database of four-dimensional reflexive polytopes. The algorithm is based on the existence of facets of Fano polytopes…

We completely describe the Fano scheme of lines for a projective toric surface in terms of the geometry of the corresponding lattice polygon.

It is pretty well-known that toric Fano varieties of dimension k with terminal singularities correspond to convex lattice polytopes P in R^k of positive finite volume, such that intersection of P and Z^k consists of the point 0 and vertices…

Gorenstein Fano polytopes arising from finite partially ordered sets will be introduced. Then we study the problem which partially ordered sets yield smooth Fano polytopes.

The purpose of this paper is to give basic tools for the classification of nonsingular toric Fano varieties by means of the notions of primitive collections and primitive relations due to Batyrev. By using them we can easily deal with…

Toric geometry provides a bridge between algebraic geometry and combinatorics of fans and polytopes. For each polarized toric variety (X,L) we have associated a polytope P. In this thesis we use this correspondence to study birational…

We prove that the Fano variety of lines of a generic cubic fourfold containing a plane is isomorphic to a moduli space of twisted stable complexes on a K3 surface. On the other hand, we show that the Fano varieties are always birational to…

The anticanonical complex generalizes the Fano polytope from toric geometry and has been used to study Fano varieties with torus action so far. We work out the case of complete intersections in toric varieties defined by non-degenerate…

We explicitly construct the smooth toric Fano variety which is isomorphic to the blow-up of the projective space at torus invariant points in codimension one by anti-flips.

We study the anti-canonical ring of a projective variety and we characterise varieties of log Fano type depending on the singularities of these models.